English
Related papers

Related papers: Parameterized Complexity of Superstring Problems

200 papers

A substring Q of a string S is called a shortest unique substring (SUS) for interval [s,t] in S, if Q occurs exactly once in S, this occurrence of Q contains interval [s,t], and every substring of S which contains interval [s,t] and is…

Discrete Mathematics · Computer Science 2017-02-21 Takuya Mieno , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

A permutation $\pi$ contains a permutation $\sigma$ as a pattern if it contains a subsequence of length $|\sigma|$ whose elements are in the same relative order as in the permutation $\sigma$. This notion plays a major role in enumerative…

Data Structures and Algorithms · Computer Science 2015-01-13 Ivan Bliznets , Marek Cygan , Pawel Komosa , Lukas Mach

We study the "set parameterized matching" problem, a generalization of the classical parameterized matching problem introduced by Baker. In set parameterized matching, both the pattern and text are sequences where each position contains a…

Data Structures and Algorithms · Computer Science 2026-05-04 Moshe Lewenstein , Ely Porat

Golovach, Paulusma and Song (Inf. Comput. 2014) asked to determine the parameterized complexity of the following problems parameterized by $k$: (1) Given a graph $G$, a clique modulator $D$ (a clique modulator is a set of vertices, whose…

Data Structures and Algorithms · Computer Science 2019-07-30 Gregory Gutin , Diptapriyo Majumdar , Sebastian Ordyniak , Magnus Wahlström

The field of kernelization studies polynomial-time preprocessing routines for hard problems in the framework of parameterized complexity. Although a framework for proving kernelization lower bounds has been discovered in 2008 and…

Data Structures and Algorithms · Computer Science 2011-11-03 Marek Cygan , Stefan Kratsch , Marcin Pilipczuk , Michał Pilipczuk , Magnus Wahlström

This paper analyzes to what extent it is possible to efficiently reduce the number of clauses in NP-hard satisfiability problems, without changing the answer. Upper and lower bounds are established using the concept of kernelization.…

Computational Complexity · Computer Science 2019-07-01 Bart M. P. Jansen , Astrid Pieterse

We consider the problem of finding a subcomplex K' of a simplicial complex K such that K' is homeomorphic to the 2-dimensional sphere, S^2. We study two variants of this problem. The first asks if there exists such a K' with at most k…

Data Structures and Algorithms · Computer Science 2019-09-10 Benjamin Burton , Sergio Cabello , Stefan Kratsch , William Pettersson

In a parameterized problem, every instance I comes with a positive integer k. The problem is said to admit a polynomial kernel if, in polynomial time, one can reduce the size of the instance I to a polynomial in k, while preserving the…

Discrete Mathematics · Computer Science 2013-09-26 Hans L. Bodlaender , Fedor V. Fomin , Daniel Lokshtanov , Eelko Penninkx , Saket Saurabh , Dimitrios M. Thilikos

In this work, we study the $k$-median clustering problem with an additional equal-size constraint on the clusters, from the perspective of parameterized preprocessing. Our main result is the first lossy ($2$-approximate) polynomial kernel…

Data Structures and Algorithms · Computer Science 2021-07-16 Sayan Bandyapadhyay , Fedor V. Fomin , Petr A. Golovach , Nidhi Purohit , Kirill Simonov

The starting point of our work is a decade-old open question concerning the subexponential parameterized complexity of \textsc{2-Layer Crossing Minimization}. In this problem, the input is an $n$-vertex graph $G$ whose vertices are…

Data Structures and Algorithms · Computer Science 2025-10-16 Fedor V. Fomin , Petr A. Golovach , Tanmay Inamdar , Saket Saurabh , Meirav Zehavi

Palindromes are important objects in strings which have been extensively studied from combinatorial, algorithmic, and bioinformatics points of views. It is known that the length of the longest palindromic substrings (LPSs) of a given string…

Data Structures and Algorithms · Computer Science 2021-01-11 Mitsuru Funakoshi , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

We consider the Consensus Patterns problem, where, given a set of input strings, one is asked to extract a long-enough pattern which appears (with some errors) in all strings. We prove that this problem is W[1]-hard when parameterized by…

Computational Complexity · Computer Science 2017-02-28 Laurent Bulteau

A superstring of a set of strings correspond to a string which contains all the other strings as substrings. The problem of finding the Shortest Linear Superstring is a well-know and well-studied problem in stringology. We present here a…

Data Structures and Algorithms · Computer Science 2021-11-18 Bastien Cazaux , Eric Rivals

This paper investigates the number of quantum queries made to solve the problem of reconstructing an unknown string from its substrings in a certain query model. More concretely, the goal of the problem is to identify an unknown string $S$…

Motivated by mass-spectrometry protein sequencing, we consider a simply-stated problem of reconstructing a string from the multiset of its substring compositions. We show that all strings of length 7, one less than a prime, or one less than…

Discrete Mathematics · Computer Science 2014-03-12 Jayadev Acharya , Hirakendu Das , Olgica Milenkovic , Alon Orlitsky , Shengjun Pan

Described are two algorithms to find long approximate palindromes in a string, for example a DNA sequence. A simple algorithm requires O(n)-space and almost always runs in $O(k.n)$-time where n is the length of the string and k is the…

Data Structures and Algorithms · Computer Science 2007-05-23 L. Allison

A {\it superpattern} is a string of characters of length $n$ that contains as a subsequence, and in a sense that depends on the context, all the smaller strings of length $k$ in a certain class. We prove structural and probabilistic results…

Combinatorics · Mathematics 2016-03-08 Yonah Biers-Ariel , Yiguang Zhang , Anant Godbole

In this paper, we study the parameterized complexity of local search, whose goal is to find a good nearby solution from the given current solution. Formally, given an optimization problem where the goal is to find the largest feasible…

Data Structures and Algorithms · Computer Science 2025-12-04 Aditya Anand , Vincent Cohen-Addad , Tommaso d'Orsi , Anupam Gupta , Euiwoong Lee , Debmalya Panigrahi , Sijin Peng

We give a near-optimal quantum algorithm for the longest common substring (LCS) problem between two run-length encoded (RLE) strings, with the assumption that the prefix-sums of the run-lengths are given. Our algorithm costs…

Quantum Physics · Physics 2024-11-06 Tzu-Ching Lee , Han-Hsuan Lin

Kernelization is a formalization of efficient preprocessing for NP-hard problems using the framework of parameterized complexity. Among open problems in kernelization it has been asked many times whether there are deterministic polynomial…

Computational Complexity · Computer Science 2015-07-14 Michael Etscheid , Stefan Kratsch , Matthias Mnich , Heiko Röglin